Answer to Question #160077 in Physics for Smayya Ruganyira

Question

A 1.2 HP motor (1 HP = 746W) is used to raise a 1300kg Land Rover 5.7m up into a tree. What time will it take?

A massless spring with a spring constant of 34N/m is compressed 5.8cm horizontally and used to shoot an 18 gram marble across a frictionless table. What is the speed of the marble?

A man of mass 70 kg climbs stairs of vertical height 2.5 m .Calculate the work done against the force of gravity. (Take g = 9.81 m s2.)

A stone of weight 10 N falls from the top of a 250 m high cliff.

(a) Calculate how much work is done by the force of gravity in pulling the, stone to the foot of the cliff.

(b)How much energy is transferred to the stone?

Calculate how much gravitational potential energy is gained if you climb a flight of stairs. Assume that you have a mass of 52 kg and that the height you lift yourself is 2.5 m.

Answer 1

1)

$$P=\dfrac{W}{t}=\dfrac{mgh}{t},$$ $$t=\dfrac{mgh}{P}=\dfrac{1300\ kg\cdot9.8\ \dfrac{m}{s^2}\cdot5.7\ m}{1.2\ HP\cdot\dfrac{746\ W}{1\ HP}}=81\ s.$$

2)

$$\dfrac{1}{2}kx^2=\dfrac{1}{2}mv^2,$$ $$v=\sqrt{\dfrac{kx^2}{m}}=\sqrt{\dfrac{34\ \dfrac{N}{m}\cdot(0.058\ m)^2}{0.018\ kg}}=2.52\ \dfrac{m}{s}.$$

3)

$$W=Fh=mgh=70\ kg\cdot9.81\ \dfrac{m}{s^2}\cdot2.5\ m=1716.75\ J.$$

4)

a)

$$W_g=F_gd=10\ N\cdot250\ m=2500\ J.$$

b) By the law of conservation of energy, the potential energy of the stone at the top of the high cliff converted into kinetic energy. Since, $\Delta KE=W_g$, $2500\ J$ of energy was transferred to the stone.

5)

$$U=mgh=52\ kg\cdot9.8\ \dfrac{m}{s^2}\cdot2.5\ m=1274\ J.$$