Mechanics | Relativity Answers

a solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 m/s.It collides with a horizontal spring of force constant 200 N/m.
what will be the maximum compression produced in spring?

a) A force F=A[(x/a)-1] is acting on a particle along the x-axis. Determine the work
done by the force in moving the particle from x = 0 to x = 2a .
b) A block of mass 6.0 kg slides from rest at a height of 2.0 m down to a horizontal surface
where it passes over a 1.5 m rough patch. After crossing this patch it climbs up another
incline which is at an angle of 30° to the ground. The rough patch has a coefficient of
kinetic friction μk = 0.25. What height does the block reach on the incline before it
comes to rest?

a) What is the maximum torque exerted by a 60 kg person riding a bike, if the rider puts all
his weight on each pedal when climbing a hill? The pedals rotate in a circle of radius
17 cm.
b) A ball of mass 1.5 kg rolling to the right with a speed of 3.6m/s, collides head-on with
a spring with a spring constant of 2.0Nm^-2.Determine the maximum compression of the
spring and the speed of the ball when the compression of the spring is 0.10 m.

a) A ball has an angular velocity of 5.0 rad/s counterclockwise. Some time later, after
rotating through a total angle of 4.5 radians, the ball has an angular velocity of
1.5 rad/s clockwise. Determine the angular acceleration, the average angular velocity
and how much time it takes for the ball to attain this velocity.
b) When a high diver wants to execute a flip in midair, she draws her legs up against her
chest. Why does this make her rotate faster? What should she do when she wants to
come out of her flip?

a) The speed of an aeroplane is 1200m/s. The engines take in 80 kg of air per second and
mix it with 40 kg of fuel. This mixture is expelled after it ignites and it moves at a
velocity of 3000m/s relative to the aeroplane. Calculate the thrust of the engine.
b) A 2400 W engine pulls a 200 kg block at constant speed up a 12.0 m long, 25.0° incline.
Determine how long does it takes to cover this distance.

a) A massless rope is stretched horizontally between two supports that are 3.0 m apart.
When an object of weight 3200 N is hung at the center of the rope, the rope is observed
to sag by 50 cm. Calculate the tension in the rope.
b) b) A ball of mass 5.0X10^-2 Kg starting from rest, falls a height of 4.0 m and then collides
with the ground. The ball bounces up to a height of 2.0 m. The collision with the ground
takes place over a time 4.0X10^-1 S Determine (i) the momentum of the ball immediately
before the collision, (ii) the momentum of the ball immediately after the collision and
(iii) the average force of the ground on the ball.

A string fixed at both ends is 8.40 m long and has a mass of 0.120 kg.It is subjected to a tension of 96.0 N and set oscil- lating.(a) What is the speed of the waves on the string? (b)What is the longest possible wavelength for a standing wave? (c) Give the frequency of that wave.

A car accelerates at a rate of 2.0 m/s2 from rest. what is the displacement?

A 125 cm length of string has mass 2.00 g and tension 7.00 N. (a) What is the wave speed for this string? (b) What is the lowest resonant frequency of this string?

Darth vader pushes luke skywalker with 17n, who then accelerates at 11m/s squared. Luke is thrown into c-3po and send him flying at a velocity of 8m/s. From this information find the mass of c-3po