How to Calculate Forces Exerted by Hands on a Shovel
What forces are exerted on the shovel by each hand?
A man holds a shovel with a downward force of 40.0 N on his right hand and an upward force of 20.0 N on his left hand. How can we determine the forces exerted by each hand on the shovel?
Calculating Forces Exerted by Each Hand
To determine the forces exerted by each hand on the shovel, we can use the principle of torque equilibrium. Since the shovel is in a horizontal position, the net torque acting on it must be zero.
The torque exerted by the man's right hand (clockwise torque) is given by the product of the force (F1) exerted by the hand and the distance (d1) between the right hand and the pivot point. Similarly, the torque exerted by the man's left hand (counterclockwise torque) is given by the product of the force (F2) exerted by the left hand and the distance (d2) between the left hand and the pivot point.
Detail Explanation
Since the net torque is zero, we have the equation: F1 × d1 = F2 × d2. Given that d1 = 0.45 m, d2 = 1.60 m, and F2 (upward force) = F1 + weight of the snow (12.0 kg × 9.8 m/s²), we can solve for F1 and F2.
Substituting the values, we can calculate: F1 × 0.45 m = (F1 + 12.0 kg × 9.8 m/s²) × 1.60 m. Simplifying the equation, we find: 0.45 F1 = 19.6 F1 + 188.16. Solving for F1, we get: F1 = 40.0 N.
Since F2 = F1 + weight of the snow, we can calculate: F2 = 40.0 N + (12.0 kg × 9.8 m/s²) = 20.0 N. Therefore, the man exerts a downward force of 40.0 N with his right hand and an upward force of 20.0 N with his left hand on the shovel.