You are holding a 5 kg dumbbell straight out at arm's length. Assuming your arm is 0.63 m long, what torque is the dumbbell exerting on your shoulder?
torque= distance*(mass*g)
To calculate the torque exerted by the dumbbell on your shoulder, we will use the equation:
Torque = Force x Distance
First, let's determine the force exerted by the dumbbell. The force exerted by an object can be calculated using the formula:
Force = mass x acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2. Given that the mass of the dumbbell is 5 kg, we can calculate the force as follows:
Force = 5 kg x 9.8 m/s^2 = 49 N
Now, let's calculate the distance from the shoulder to the center of mass of the dumbbell. Since your arm is fully extended, the distance from the shoulder to the center of mass of the dumbbell is equal to the length of your arm, which is given as 0.63 m.
Torque = Force x Distance
Torque = 49 N x 0.63 m
Calculating the torque:
Torque = 30.87 Nm
Therefore, the torque exerted by the dumbbell on your shoulder is 30.87 Nm.
To calculate the torque exerted by a dumbbell on your shoulder, you need to know two things: the force exerted by the dumbbell and the distance between the point where the force is applied (in this case, your hand) and the axis of rotation (in this case, your shoulder).
In this scenario, the force exerted by the dumbbell is equal to its weight, which can be calculated using the formula:
Force = Mass × acceleration due to gravity
Given that the mass of the dumbbell is 5 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can find the force:
Force = 5 kg × 9.8 m/s^2 = 49 N
Next, we need to find the distance between the point where the force is applied (your hand) and the axis of rotation (your shoulder). In this case, the distance is equal to the length of your arm, which is specified as 0.63 m.
With both the force and the distance known, we can calculate the torque using the formula:
Torque = Force × distance
Torque = 49 N × 0.63 m = 30.87 N·m
Therefore, the dumbbell is exerting a torque of 30.87 N·m on your shoulder.