kindly answer all these

A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass m 1 5 48.0 kg travels in the positive x - direction at 12.0 m/s, and a second piece of mass m 2 5 62.0 kg travels in the xy-plane at an angle of 105 at 15.0 m/s. The third piece has mass m 3 5 112 kg. (a) Sketch a diagram of the situation, labeling the different masses and their velocities. (b) Write the general expression for conservation of momentum in the x- and y-directions in terms of m 1, m 2, m 3, v 1, v 2, and v 3 and the sines and cosines of the angles, taking u to be the unknown angle. (c) Calculate the final x-components of the momenta of m 1 and m 2. (d) Calculate the final y-components of the momenta of m 1 and m 2. (e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the known mass m 3. (f) Solve the two momentum equations for v 3 cos u and v 3 sin u, respectively, and use the identity cos2 u 1 sin2 u 5 1 to obtain v 3. (g) Divide the equation for v 3 sin u by that for v 3 cos u to obtain tan u, then obtain the angle by taking the inverse tangent of both sides. (h) In general, would three such pieces necessarily have to move in the same plane? Why?

A cylinder of volume 0.300 m3m3 contains 10.0 molmol of neon gas at 20.020.0 C. Assume neon behaves as an ideal gas. (a) What is the pressure of the gas? (b) Find the internal energy of the gas, (c) Suppose the gas expands at constant pressure to a volume of 1.000 m3.m3. How much work is done on the gas? (d) What is the temperature of the gas at the new volume? (e) Find the internal energy of the gas when its volume is 1.000 m3.(1)m3.(1) Compute the change in the internal energy during the expansion. (g) Compute UWUW (h) Must thermal energy be transferred to the gas during the constant pressure expansion or be taken away? (i) Compute QQ , the thermal energy transfer. (j) What symbolic relationship between Q,Q, U,U, and WW is suggested by the values obtained?

Sketch a PVPV diagram and find the work done by the gas during the following stages. (a) A gas is expanded from a volume of 1.0 LL to 3.0 LL at a constant pressure of 3.0 atm.atm. (b) The gas is then cooled at constant volume until the pressure falls to 2.0 atm. (c) The gas is then compressed at a constant pressure of 2.0 atm from a volume of 3.0 LL to 1.0 LL . Note: Be careful of signs. (d) The gas is heated until its pressure increases from 2.0 atm to 3.0 atmatm at a constant volume. (e) Find the net work done during the complete cycle.

An unstable nucleus of mass 1.71026kg,1.71026kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of m1=5.0m1=5.0 1027kg1027kg , moves in the positive yy direction with speed v1=v1= 6.0106m/s6.0106m/s . Another particle, of mass m2=8.41027kg,m2=8.41027kg, moves in the positive xx -direction with speed v2=4.0106v2=4.0106 v2=4.0106v2=4.0106 m/sm/s . Find the magnitude and direction of the velocity of the third particle.

An amateur skater of mass M is trapped in the middle of an ice rink and is unable to return to the side where there is no ice. Every motion she makes causes her to slip on the ice and remain in the same spot. She decides to try to return to safety by removing her gloves of mass m and throwing them in the direction opposite the safe side. (a) She throws the gloves as hard as she can, and they leave her hand with a velocity vgloves. Explain whether or not she moves. Ifvgloves. Explain whether or not she moves. If If she does move, calculate her velocity v girl relative to the Earth after she throws the gloves. (b) Discuss her motion from the point of view of the forces acting on her.

A tennis ball of mass 57.0 g is held just above a basketball of mass 590 g. With their centers vertically aligned, both balls are released from rest at the same time, falling through a distance of 1.20 m, as shown in Figure P6.45. (a) Find the magnitude of the basketball's velocity the instant before the basketball reaches the ground. (b) Assume that an elastic collision with the ground instantaneously reverses the velocity of the basketball so that it collides with the tennis ball just above it. To what height does the tennis ball rebound?

A 1200-kg car traveling initially with a speed of 25.0 m/s in an easterly direction crashes into the rear end of a 9 000-kg truck moving in the same direction at 20.0 m/s (Fig. P6.44). The velocity of the car right after the collision is 18.0 m/s to the east. (a) What is the velocity of the truck right after the collision? (b) How much mechanical energy is lost in the collision? Account for this loss in energy.

In research in cardiology and exercise physiology, it is often important to know the mass of blood pumped by a person's heart in one stroke. This information can be obtained by means of a ballistocardiograph. The instrument works as follows: The subject lies on a horizontal pallet floating on a film of air. Friction on the pallet is negligible. Initially, the momentum of the system is zero. When the heart beats, it expels a mass m of blood into the aorta with speed v, and the body and platform move in the opposite direction with speed V. The speed of the blood can be determined independently (e.g., by observing an ultrasound Doppler shift). Assume that the blood's speed is 50.0 cm/s in one typical trial. The mass of the subject plus the pallet is 54.0 kg. The pallet moves at a speed of 6.00 3 1025m in 0.160 s after one heartbeat. Calculate the mass of blood that leaves the heart. Assume that the mass of blood is negligible compared with the total mass of the person. This simplified example illustrates the principle of ballistocardiography, but in practice a more sophisticated model of heart function is used.

Most of us know intuitively that in a head-on collision between a large dump truck and a subcompact car, you are better off being in the truck than in the car. Why is this? Many people imagine that the collision force exerted on the car is much greater than that exerted on the truck. To substantiate this view, they point out that the car is crushed, whereas the truck is only dented. This idea of unequal forces, of course, is false; Newton's third law tells us that both objects are acted upon by forces of the same magnitude. The truck suffers less damage because it is made of stronger metal. But what about the two drivers? Do they experience the same forces? To answer this question, suppose that each vehicle is initially moving at 8.00 m/s and that they undergo a perfectly inelas- tic head-on collision. Each driver has mass 80.0 kg. Including the masses of the drivers, the total masses of the vehicles are 800 kg for the car and 4.00103kg4.00103kg for the truck. If the col- lision time is 0.120 s, what force does the seat belt exert on each driver?

A cannon is rigidly attached to a carriage, which can move along horizontal rails, but is connected to a post by a large spring, initially unstretched and with force constant k=k= 2.00104N/m,2.00104N/m, as in Figure P6.75P6.75 . The cannon fires a 200102kg200102kg projectile at a velocity of 125 m/sm/s directed 45.045.0 above the horizontal. cannon and its carriage is 5.00103kg5.00103kg , find the recoil speed of the cannon. (b) Determine the maximum extension of the spring. (c) Find the maximum force the spring exerts on the carriage. (d) Consider the system consisting of the cannon, the carriage, and the shell. Is the momentum of this system conserved during the firing? Why or why not?

A boy of mass mbmb and his girlfriend of mass mFmF , both wearing ice skates, face each other at rest while standing on a frictionless ice rink. The boy pushes the girl, giving her a velocity vgvg toward the east. Assume that mb>mKmb>mK (a) Describe the subsequent motion of the boy. (b) Find expressions for the final kinetic energy of the girl and the final kinetic energy of the boy, and show that the girl has greater kinetic energy than the boy. (c) The boy and girl had zero kinetic energy before the boy pushed the girl, but ended up with kinetic energy after the event. How do you account for the appearance of mechanical energy?

A man of mass m1=70.0kgm1=70.0kg is skating at v1=8.00m/sv1=8.00m/s behind his wife of mass m2=50.0kg,m2=50.0kg, who is skating at v2=4.00m/sv2=4.00m/s . Instead of passing her, he inadvertently collides with her. He grabs her around the waist, and they maintain their balance. (a) Sketch the problem with before-and-after diagrams, representing the skaters as blocks. (b) Is the collision best described as elastic, inelastic, or perfectly inelastic? Why? (c) Write the general equation for conservation of momentum in terms of m1,v1,m2,v2,m1,v1,m2,v2, and final velocity vj,vj, (d) Solve the momentum equation for vf,(c)vf,(c) Substitute valucs, obtaining the numerical value for vf,vf, their speed after the collision.

Q C Drops of rain fall perpendicular to the roof of a parked car during a rainstorm. The drops strike the roof with a speed of 12 m/s, and the mass of rain per second striking the roof is 0.035 kg/s. (a) Assuming the drops come to rest after striking the roof, find the average force exerted by the rain on the roof. (b) If hailstones having the same mass as the raindrops fall on the roof at the same rate and with the same speed, how would the average force on the roof compare to that found in part (a)?

An ideal gas expands at constant pressure. (a) Show that PV=nRTPV=nRT . (b) If the gas is monatomic, start from the definition of internal energy and show that U=32Wew,U=32Wew, where Wcny is the work done by the gas on its environment.(c)Wcny is the work done by the gas on its environment.(c) For the same monatomic ideal gas, show with the first law that Q=52WenvQ=52Wenv (d) Is it possible for an ideal gas to expand at constant pressure while exhausting thermal energy? Explain.

An ideal monatomic gas is contained in a vessel of constant volume 0.200 m3m3 . The initial temperature and pressure of the gas are 300.K300.K and 5.00 atmatm , respectively. The goal of this problem is to find the temperature and pressure of the gas after 16.0 kJkJ of thermal energy is supplied to the gas. (a) Use the ideal gas law and initial conditions to calculate the number of moles of gas in the vessel. (b) Find the specific heat of the gas. (c) What is the work done by the gas during this process? (d) Use the first law of thermodynamics to find the change in internal energy of the gas. (e) Find the change in temperature of the gas. (f) Calculate the final temperature of the gas. (g) Use the ideal gas expression to find the final pressure of the gas.