Search & Filtering
Starting at the top of the hill, Eric rides his mountain bike down to the bottom of the hill. Friction acts on him the entire time. What can be known about his mechanical energy?
A small mass m attached to the end of a string revolves in a circle on a frictionless tabletop. The other end of the string passes through a hole in the table. Initially, the mass revolves with a speed v=2.4m/s in a circle of radius R1=0.8m. The string is then pulled slowly through the hole so that the radius is reduced to R=0.48m. What is the speed, V2, of the mass now?
. A 3 kg object travels in a uniform circle at a constant speed of 10 m/s. The centripetal force acting on the object is 150 Newtons.
a. Calculate the weight of the object.
b. Calculate the centripetal acceleration of the object.
c. Calculate the radius of the circle.
d. Calculate the circumference of the circle.
e. Calculate the time required for the object to complete one full circle.
A crate of mass 40.0 kg is pulled by a force of 2000 N, up an inclined plane which
makes an angle of 30º with the horizon. The coefficient of kinetic friction between the
plane and the crate is miu.k = 0.20. If the crates starts from rest, calculate its speed after it
has been pulled 10.0 m. Draw the free body diagram. Take
g=10.0 ms-² .
Discharging RC circuit. • In the RC circuit shown, the battery has fully charged the capacitor, so Q0 = C E. Then at t = 0 the switch is thrown from position a to b. The battery emf is 20.0 V, and the capacitance C = 1.02 μF. The current I is observed to decrease to 0.50 of its initial value in 40 μs. (a) What is the value of Q, the charge on the capacitor, at t = 0? (b) What is the value of R? (c) What is Q at t = 60 μs?
RC Circuit, with EMF. • The capacitance in the circuit shown is C = 0.30 μF, the total resistance is R = 20 kΩ, the battery emf is E = 12 V. Calculate: (a) the time constant, (b) the maximum charge the capacitor could acquire, (c) the time it takes for the charge to reach 99% of this value, (d) the current I when the charge Q is half its maximum value, (e) the maximum current, (f) the charge Q when the current I is 0.20 of its maximum value.
A soccer player kicks a ball at an angle of 37 degree from the horizontal with an initial speed
of 50 ft/sec. Assume that the ball moves in a vertical plane. a) Find the time t1 at which the
ball reaches the highest point of its trajectory. b) How high does the ball go? c) What is the
horizontal range of the ball and how long is it in the air? d) What is the velocity of the ball as
it strikes the ground?
A particle of mass m is attached to the end of a string and moves in a circle of radius of
radius r on a frictionless horizontal table. The string passes through a frictionless hole in the
table and, initially, the other end id fixed. a) if the string is pulled so that the radius of the
circular orbit decreases, how does the angular velocity change if it is ω0 when r = r0? b) what
work is done when the particle is pulled slowly in from a radius r0 to a radius r0/2?
A spaceship of mass m has velocity v in the positive x direction of an inertial reference
frame. A mass dm is fired out the rear of the ship with constant exhaust velocity (-v0) with
respect to the spaceship. a) using conservation of momentum, show that dv/v0 = dm/m, b)
By integration, find the dependence of v on m if v1 and m1 are the initial values. c) Can the
acceleration be constant if dm/dt, the burning rate is constant.
The Earth and the Moon may be considered to be uniform spheres that are isolated in space. The Earth has radius R and mean density ρ. The Moon, mass m, is in a circular orbit about the Earth with radius nR,
The Moon makes one complete orbit of the Earth in time T.
Show that the mean density ρ of the Earth is given by the expression
ρ = 3πn^3/GT^2
