Question

1) A stone with mass 240 g is swirled around using a 0.2 m long rope such that it makes 10 full revolutions in 17 seconds. a) The speed of the stone is v = m/s. b) The tension in the rope is T = N. c) Work done by the tension force is W = J.

2) A puck is kicked up an icy incline with an initial speed of 3.4 m/s. The angle of the incline is 31 °. The kinetic coefficient of friction of the puck on ice is μ = 0.15.
a) The time it take for the puck to go up and come back down is t =  s.
b) The maximum distance traveled by the puck up the incline until is d =  m.
c) Find the maximum elevation the puck goes up the incline by using the principle of conservation of energy. The height h =  m.

3) The electricity price is 10 cents per kWh. What is the monthly cost of electricity for running a light bulb that consumes 70 J per second for 6 hours per day? The cost is $ ___

4) The work done by a force given by  = 2 x³  + 7 y²  N that acts on an object that moves along the y axis from y_i = 4 m to y_f = 6 m is  J.

Answer 1

1) Given mass of the stone m = 240g = 240 x 10-3kg, radius of the rope r = 0.2m and it makes 10 revolutions in 17 seconds. So its frequency is given by

(a) We know that the angular velocity is given by

Now the angular velocity and speed (v) is related by

So the speed of the stone is 0.74m/s.

(b) The tension (T) in the rope provides the necessary centripetal force for the swirling of the stone. So

The tension in the rope is 0.66N.

(c) The tension (T) is action towards the centre and the displacement (S) of the stone is towards the tangent. So the angle between them is 90. The work done (W) is given by.

Hence no work is done by the tension.

2) Given the initial speed of the puck is u = 3.4m/s, the angle of inclination is = 31 and the coefficient of kinetic friction = 0.15.

(a) Acceleration of a body moving up in a rough inclined surface is given by

With this initial velocity, the particle moves up some distance up the incline and stops. So final velocity v = 0. So the time taken by the upward journey is

It took 0.44 seconds to go up the incline. Now the total time taken by the puck to go up and come down is,

The time taken for the puck to go up and come down is 1.08s.

(c) Let the maximum distance travelled by the puck up the incline is S. Then

The puck travels 0.92m up the incline.

(d) If h is the maximum height travelled by the puck then, by principle of conservation of energy

Initial Kinetic energy + Initial Potential energy = Final kinetic energy + Final potential energy

The maximum elevation the puck goes up the incline is 0.59m.

3) Given the energy consumption per second = 70J

So the erergy consumption for 6 hours a day is = 70 x 6hrs = 70 x 216000seconds = 1512000J

The energy consumption for a month of 30 days is = 1512000 x 30 = 45360000J

We know that 1 Joule = 3.6 x 106 kWh

So the energy consumption (E) in kWh for 30 days is

The cost of electricity for 1 kWh is 10 cents. So the cost of 12.6kWh of electricity is

(4) Given a force (F)

The work done (W) by the force from yi = 4m to yf = 6m is

The work done by the force from yi = 4m to yf = 6m is 366.67J.