A 10-kg ladder 2.5m long rests agaist a frictionless wall with its base on the floor 80cm from the wall. How much force does the top of the ladder exert on the wall?
To determine the force that the top of the ladder exerts on the wall, we can use Newton's second law and the concept of torque.
First, let's calculate the torque exerted by the ladder about the base. Torque is defined as the force multiplied by the lever arm, where the lever arm is the perpendicular distance between the axis of rotation (the base) and the line of action of the force.
In this case, the force is the weight of the ladder, which can be calculated using the formula: weight = mass * acceleration due to gravity.
The mass of the ladder is given as 10 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the weight of the ladder is 10 kg * 9.8 m/s^2 = 98 N.
The lever arm is the distance between the base of the ladder and the point where the force is applied. In this case, it is given as 80 cm or 0.8 m.
Now, we can calculate the torque by multiplying the force and the lever arm: torque = force * lever arm = 98 N * 0.8 m = 78.4 Nm.
Since the ladder is in equilibrium (not rotating), the torque exerted by the ladder about the base must be balanced by the torque exerted by the top of the ladder on the wall. This means that the force exerted by the top of the ladder on the wall is equal in magnitude but opposite in direction to the torque.
Therefore, the force exerted by the top of the ladder on the wall is also 78.4 N in the opposite direction.