1. A box that weighs 50 kg is pulled 7 m up an inclined plane with a force on 250 N to a vertical height on 3 m. Calculate the mechanical efficiency of this machine.
Wo= F x D
Wo= 500 N x 3 m
Wo+ 1, 500 J
Wi= F x D
Wi= 250 N x 7 m
Wi= 1, 750 J
ME= Wo mmmWi ME= 1,500 J mmm1, 750 J ME= 86%
2. Why is the mechanical efficiency of a machine always less than 100%?
This is because some of the work used to make the machine function goes toward overcoming the friction of the machine due to its moving parts.
3. Explain how adding wheels and lubricants to a machine can help improve its efficiency?
Adding wheels improve mechanical efficiency because it reduces the friction because there is only the bottom surface of the wheel touching the ground at any one time, and if friction decreases mechanical efficiency increases. Putting lubricants on a machines parts can increase its mechanical efficiency because it also reduces friction, it reduces friction because the lubricants allow the machines parts to slide past one another smoother, meaning that the parts don't stick together as much and it creates less heat.
4. It takes 700 J of energy to lift a box to a vertical height of 3 m. Determine which of the following systems would give the greatest mechanical efficiency to perform this task and should therefore be used.
a) The effort arm of a lever is pushed through 5 m with a force of 175 N.
Wi= 175 N x 5 m
Wi= 875 J
b) The box is pushed up 8 m with a force of 120 N.
Wi= 120 N x 8 m
WI= 960 J
c) A force of 120 N is exerted on the rope of a pulley, which is attached to the box, and the rope moves 6 m.
Wi= 120 N x 6 m
Wi= 720 J
5. A lever is used to lift a box to a vertical height of 20 cm. 40 N of force are applied through 50 cm to do this. How much energy is wasted as heat? (The force of gravity acting on the box is 75 N.)
Wo= F x D
Wo= 75 N x 0.2 m
Wo= 15 J
Wi= F x D
Wi= 40 x 0.5
Wi= 20 J
Energy Wasted as Heat = Wi - Wo
Energy Wasted as Heat = 20 J - 15 J
Energy Wasted as Heat = 5 J
6. It takes 250 N to pull a cart up a 10 m inclined plane to a vertical height of 2.5 m. The force of gravity acting on the cart is 600 N. Determine the efficiency of the machine to the nearest whole number.
1. A box that weighs 50 kg is pulled 7 m up an inclined plane with a force on 250 N to a vertical height on 3 m. Calculate the mechanical efficiency of this machine.
Wo= F x D
Wo= 500 N x 3 m
Wo+ 1, 500 J
Wi= F x D
Wi= 250 N x 7 m
Wi= 1, 750 J
ME= Wo
mmmWi
ME= 1,500 J
mmm1, 750 J
ME= 86%
2. Why is the mechanical efficiency of a machine always less than 100%?
This is because some of the work used to make the machine function goes toward overcoming the friction of the machine due to its moving parts.
3. Explain how adding wheels and lubricants to a machine can help improve its efficiency?
Adding wheels improve mechanical efficiency because it reduces the friction because there is only the bottom surface of the wheel touching the ground at any one time, and if friction decreases mechanical efficiency increases. Putting lubricants on a machines parts can increase its mechanical efficiency because it also reduces friction, it reduces friction because the lubricants allow the machines parts to slide past one another smoother, meaning that the parts don't stick together as much and it creates less heat.
4. It takes 700 J of energy to lift a box to a vertical height of 3 m. Determine which of the following systems would give the greatest mechanical efficiency to perform this task and should therefore be used.
a) The effort arm of a lever is pushed through 5 m with a force of 175 N.
Wi= 175 N x 5 m
Wi= 875 J
b) The box is pushed up 8 m with a force of 120 N.
Wi= 120 N x 8 m
WI= 960 J
c) A force of 120 N is exerted on the rope of a pulley, which is attached to the box, and the rope moves 6 m.
Wi= 120 N x 6 m
Wi= 720 J
5. A lever is used to lift a box to a vertical height of 20 cm. 40 N of force are applied through 50 cm to do this. How much energy is wasted as heat? (The force of gravity acting on the box is 75 N.)
Wo= F x D
Wo= 75 N x 0.2 m
Wo= 15 J
Wi= F x D
Wi= 40 x 0.5
Wi= 20 J
Energy Wasted as Heat = Wi - Wo
Energy Wasted as Heat = 20 J - 15 J
Energy Wasted as Heat = 5 J
6. It takes 250 N to pull a cart up a 10 m inclined plane to a vertical height of 2.5 m. The force of gravity acting on the cart is 600 N. Determine the efficiency of the machine to the nearest whole number.
Wo= 600 N x 2.5 m
Wo= 1, 500 J
Wi= 250 N x 10 m
WI= 2, 500
ME= Wo
vvvvWi
ME= 1, 500 J
mmm2, 500 J
ME= 60 %