Mechanics | Relativity Answers

John is riding a bicycle and comes across a hill of height 7.30 m. At the base of the hill, he is traveling at 6.00 m/s. When he reaches the top of the hill, he is traveling at 1.00 m/s. Jonathan and his bicycle together have a mass of 85.0 kg. Ignore friction in the bicycle mechanism and between the bicycle tires and the road.

i) What is the total external work done on the system of Jonathan and the bicycle between the time he starts up the hill and the time he reaches the top? ii) What is the change in potential energy stored in Jonathan’s body during this process?

In the system shown, a horizontal force Fx = 40 N acts on an object of mass m2 = 8.00 kg. A friction force fk = 5 N acts between object m2 and the table top, and m1 = 2.00 kg. i) Calculate the acceleration of the masses. ii) Calculate the tension in the string.

A roller derby car with a mass of 120kg starts at the top of the hill (20 meters high) how fast is the car going at point B with a height of 15 meters? (use g = 10m/s/s and create a LOL to help solve the problem)

1. A train of total mass 300 tonnes (3 × 105 kg) is moving up an incline of angle θ to the horizontal, where
sin θ =
1
280 . The resistance to motion is 3000 N and the train is accelerating at 0.2 ms−2
. Find
(a) the driving force of the engine,
(b) the power exerted by the driving force at the moment when the speed is 10 ms−1
.
(c) the work done by gravity when the train has moved a distance of 28 m.
2. A 54.4 kg box is being pushed a distance of 8.27m across the floor by a force F whose magnitude is 163 N.
The force F is parallel to the displacement of the box. The coefficient of kinetic friction is 0.227. Take
g = 9.81 ms−2
. Determine the work done on the box by
(a) the applied force.
(b) the friction force.
(c) the normal force.
(d) by the force of gravity.

A table-tennis ball of radius 0.041mm rolls on the inside of a track of radius 0.448cm. If the ball starts from rest at the vertical edge of the track, what will it's speed be when it reaches the lowest point of the track, rolling without slipping?

A block of mass 2.01kg is at rest on a horizontal,frictionless surface. On one side a relaxed spring with a spring constant 192N/m connects it to a wall, on the other side of light string passing over a frictionless pulley connects it to the hanging block with a mass of 4.02kg. The pulley has a moment of inertia 0.006kg per square meter and a radius of 0.055m. A short time after the hanging block is released from rest it has fallen through a height of 0.09m.
a) determine the combined total kinetic energy of the blocks-and -pulley system,and
b)the rotational kinetic energy of the pulley.

A flywheel has a moment of inertia of 1.6 × 10−3 kg.m2
. When a constant torque is
applied, it reaches an angular velocity of 1200 rev/min in 15 s. Assuming it started from
rest, find:
i) the angular acceleration
ii) the unbalanced torque applied
iii) the angle turned through 15 s
iv) the work done on the flywheel by the torque

A 9.00 kg object, travelling South with a speed of 8.50 m/s, is moving towards a 12.0 kg
object that is moving East with a speed of 6.00 m/s. Determine the total momentum

What is the angular momentum of a figure skater spinning at 3.0 rev/s with arms in close to her body,
assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 48 kg ?
How much torque is required to slow her to a stop in 4.0 s, assuming she does not move her arms?

A solid shaft of 10cm diameter transmits 74 kW at 150 rev/min. Calculate (a) the
torque on the shaft, (b) the maximum shear stress developed, (c) the angle of twist in a
length of 1.50m, and (d) the shear stress at a radius of 3cm. Take G = 8 MN/cm2