1)when a person stands on bathroom scales the scale reads 60 kg. Suppose the person stands on the same scales when in an elevator (lift).
the elevator accelerates upwards at 2m/s2. Determine the new reading on the scale.
2)When a golfer strikes a golf ball it is in contact with the club head for about 1 ms and the ball leaves the club head with a speed of about 70m/s. If the mass of the ball is 50 g estimate the maximum accelerating force exerted on the golf ball, stating any assumptions that you make.
To determine the new reading on the bathroom scale when a person stands in an accelerating elevator, we need to consider the effect of the acceleration on the person's weight.
1) The person's weight can be calculated using the equation: Weight = mass * acceleration due to gravity (W = mg). Given that the scale reads 60 kg, we can assume that is the person's mass.
First, we need to calculate the weight of the person while standing still:
Weight = 60 kg * 9.8 m/s^2 = 588 N
Next, we need to consider the acceleration of the elevator, which is 2 m/s^2. When the elevator accelerates upwards, it exerts an additional force on the person. This force is equal to the mass of the person multiplied by the acceleration of the elevator.
Additional force = mass * acceleration of elevator
Additional force = 60 kg * 2 m/s^2 = 120 N
Now, we can calculate the new total force exerted on the person in the elevator:
Total force = Normal force + Additional force
Total force = 588 N + 120 N = 708 N
Therefore, the new reading on the bathroom scale in the accelerating elevator would be 708 N or approximately 70.8 kg.
2) To estimate the maximum accelerating force exerted on the golf ball when struck by a golfer, we need to consider the concept of impulse. Impulse is defined as the change in momentum of an object and can be calculated by multiplying the force applied to an object by the time period over which the force is applied.
Given that the golf ball is in contact with the club head for approximately 1 ms (0.001 seconds) and leaves the club head with a speed of 70 m/s, we need to determine the change in momentum.
Momentum = mass * velocity
Initial momentum = 0 kg.m/s (since the ball starts with zero speed)
Final momentum = 0.05 kg * 70 m/s (mass of the ball is 50 g or 0.05 kg)
Change in momentum = Final momentum - Initial momentum
Change in momentum = (0.05 kg * 70 m/s) - 0 kg.m/s
Change in momentum = 3.5 kg.m/s
Now, we can calculate the maximum accelerating force using the formula:
Maximum force = Change in momentum / Time
Maximum force = 3.5 kg.m/s / 0.001 s
Maximum force ≈ 3500 N (or 3.5 kN)
The maximum accelerating force exerted on the golf ball, during the 1 ms contact time with the club head, would be approximately 3500 N or 3.5 kilonewtons.
It is important to note that these calculations are estimates and can vary based on factors such as the efficiency of the transfer of energy from the club head to the ball and other external factors.