An 88.9 kg weight lifter is required to perform a snatch movement for their final lift in a weight lifting competition. The standard weight lifting bar is 20 kg and the load attached to the bar was in the form of 6 x 20 kg weight discs, 2 x 10 kg weight discs, 2 x 5 kg weight discs and 2 x 1.25 kg weight discs, with the discs evenly distributed on either side of the bar. The tallest weight disc was 50 cm and the bar was loaded in the centre of the tallest disc and then each subsequent disc was loaded. The snatch lift required the fully loaded bar to be moved from the floor to the competitors lifting height of 2.72 m. The successful lift was completed in 1.48 s. At the completion of the lift the weight lifter is standing on both feet with the load above the head, the weight lifters specialized shoes contact the ground with an area of 13 cm2.
(a) What was the weight of the weight lifter?
(b) How much work was done by the weight lifter?
(c) How much power was developed by the weight lifter?
(d) How much momentum did the lift produce?
(e) When the weight was held overhead what was the potential energy?
(f) What was the kinetic energy at this point?
(g) How much pressure is being exerted on the weight lifter as they stand with the load?
(a) The weight of the weight lifter is given as 88.9 kg.
(b) The total weight of the bar and plates can be calculated as follows:
Weight of the bar = 20 kg
Weight of the 6 x 20 kg weight discs = 6 x 20 kg = 120 kg
Weight of the 2 x 10 kg weight discs = 2 x 10 kg = 20 kg
Weight of the 2 x 5 kg weight discs = 2 x 5 kg = 10 kg
Weight of the 2 x 1.25 kg weight discs = 2 x 1.25 kg = 2.5 kg
Total weight = Weight of the lifter + Weight of the bar + Sum of all weight discs
Total weight = 88.9 kg + 20 kg + 120 kg + 20 kg + 10 kg + 2.5 kg
Total weight = 261.4 kg
Therefore, the weight of the bar and plates is 261.4 kg.
(c) The work done by the weight lifter can be calculated using the formula:
Work = Force x Distance
The force applied by the weight lifter is equal to the weight being lifted, which is the total weight calculated in part (b). The distance is the lifting height, given as 2.72 m. Therefore, the work done is:
Work = 261.4 kg x 9.8 m/s^2 x 2.72 m
Work = 6745.98 J
Therefore, the work done by the weight lifter is 6745.98 J.
(d) Momentum is defined as the product of mass and velocity. Since it is not given, we will assume that the weight lifter lifts the weight with a constant velocity. In this case, the momentum produced would be zero, as there is no change in velocity.
(e) The potential energy when the weight is held overhead can be calculated using the formula:
Potential Energy = Mass x Gravity x Height
The mass is the total weight calculated in part (b). The gravity is 9.8 m/s^2 and the height is the lifting height, given as 2.72 m. Therefore, the potential energy is:
Potential Energy = 261.4 kg x 9.8 m/s^2 x 2.72 m
Potential Energy = 7111.1968 J
Therefore, the potential energy when the weight is held overhead is 7111.1968 J.
(f) The kinetic energy at this point is zero, as the weight lifter is no longer in motion.
(g) Pressure is defined as force divided by area. The force in this case is the weight being lifted, which is the total weight calculated in part (b). The area is given as 13 cm^2, which needs to be converted to m^2. Therefore, the pressure is:
Pressure = (261.4 kg x 9.8 m/s^2) / (13 cm^2 x 0.0001 m^2/cm^2)
Pressure = 201945.736 N / 0.0013 m^2
Pressure = 155342102.5641 Pa
Therefore, the pressure being exerted on the weight lifter as they stand with the load is 155342102.5641 Pa.
To answer these questions, we'll need to use several principles from physics. Let's go through each question step by step.
(a) What was the weight of the weight lifter?
To find the weight of the weight lifter, we just need to use the given information that the weight lifter is 88.9 kg.
(b) How much work was done by the weight lifter?
Work is defined as the amount of force applied over a distance. In this case, the work done by the weight lifter is equal to the force applied multiplied by the distance moved. To calculate the force, we need to know the acceleration due to gravity, which is approximately 9.8 m/s². The distance moved is the height from the floor to the lifting height, which is 2.72 m. The force applied can be calculated using the formula F = m * g, where m is the mass and g is the acceleration due to gravity.
(c) How much power was developed by the weight lifter?
Power is defined as the rate at which work is done. It can be calculated by dividing the work done by the time it took to perform the work. In this case, we know the work done from part (b) and the time it took to complete the lift is given as 1.48 s.
(d) How much momentum did the lift produce?
Momentum is defined as the product of an object's mass and its velocity. In this case, the lift produces both translational and rotational momentum. To calculate the translational momentum, we need to multiply the mass of the lifted load by its velocity. The rotational momentum can be calculated based on the rotational inertia and angular velocity.
(e) When the weight was held overhead, what was the potential energy?
Potential energy is the energy an object possesses due to its position relative to other objects. In this case, the potential energy is equal to the weight of the lifted load multiplied by the height it was raised.
(f) What was the kinetic energy at this point?
Kinetic energy is the energy an object possesses due to its motion. At this point, the kinetic energy is zero since the load is held overhead and not in motion.
(g) How much pressure is being exerted on the weight lifter as they stand with the load?
Pressure is defined as the force applied per unit area. In this case, we can calculate the pressure by dividing the force applied by the contact area of the weight lifter's shoes.
By following these steps and using the given information, we can calculate the answers to each question.