1. The efficiency of a squeaky pulley system is 73 percent. The pulleys are used to raise a mass to a certain height. What force is exerted on the machine if a rope is pulled 18.0 m in order to raise a 58 kg mass a height of 3.0 m?
Answer: 13.24 N?
A person lifts a 950 N box by pushing it up an incline. If the person exerts a force of 350 N along the incline, what is the mechanical advantage of the incline?
Answer: 2.71?
1. There is an ideal mechanical advantage of 18/3 = 6 in this case. The ideal force required to balance the Mg = 58*9.8 = 568.4 N weight would be 568.4/6 = 94.7 N. Because of the 73% efficiency, the actual force required is 1/0.73 = 1.37 times higher, or 129.7 N
2. 2.71 is correct
130 N
1. To calculate the force exerted on the pulley system, we first need to find the ideal force required to lift the mass. The ideal mechanical advantage of the system is calculated by dividing the height the mass is lifted (3.0 m) by the distance the rope is pulled (18.0 m).
Ideal Mechanical Advantage = Height / Distance = 3.0 m / 18.0 m = 1/6
Next, we need to calculate the weight of the mass being lifted. The weight is equal to the mass (58 kg) multiplied by the acceleration due to gravity (9.8 m/s^2).
Weight = Mass * Acceleration due to gravity = 58 kg * 9.8 m/s^2 = 568.4 N
The ideal force required to balance the weight is calculated by dividing the weight by the ideal mechanical advantage.
Ideal Force = Weight / Ideal Mechanical Advantage = 568.4 N / (1/6) = 3410.4 N
However, the efficiency of the pulley system is given as 73%. To find the actual force required, we divide the ideal force by the efficiency (expressed as a decimal).
Actual Force = Ideal Force / Efficiency = 3410.4 N / 0.73 = 4673.15 N
Therefore, the force exerted on the machine is approximately 4673.15 N.
2. The mechanical advantage of an incline is calculated by dividing the length of the incline by the height of the incline.
Mechanical Advantage = Length / Height
In this case, we are given that the person exerts a force of 350 N along the incline and the weight of the box is 950 N. Since the person is able to lift the box, the force exerted along the incline is equal to the weight of the box.
Mechanical Advantage = 350 N / 950 N = 0.3684
Therefore, the mechanical advantage of the incline is approximately 0.3684.
To find the force exerted on the machine in the first question, we first need to calculate the ideal force required to balance the weight of the mass. The ideal mechanical advantage can be determined by dividing the distance the rope is pulled (18.0 m) by the height the mass is raised (3.0 m), which gives us a value of 6.
Next, we calculate the weight of the mass by multiplying the mass (58 kg) by the acceleration due to gravity (9.8 m/s^2), which gives us a value of 568.4 N. The ideal force required to balance this weight would be the weight divided by the ideal mechanical advantage, which gives us 568.4 N / 6 = 94.7 N.
However, because the pulley system is only 73% efficient, the actual force required is 1 divided by the efficiency (1 / 0.73 = 1.37) times higher than the ideal force. Therefore, the actual force required is 94.7 N * 1.37 = 129.7 N.
So, the force exerted on the machine is 129.7 N.
For the second question, the mechanical advantage of the incline can be calculated by dividing the force exerted by the person (350 N) by the weight of the box (950 N). This gives us a mechanical advantage of 350 N / 950 N = 0.368.
Therefore, the mechanical advantage of the incline is approximately 0.368, or 2.71 when expressed as a ratio (i.e., 2.71:1).