A 5kg steel block slides down a vertical wooden wall while you push on it with a force F at 40° to the horizontal.The coefficient of kinetic friction between the sliding surfaces is 0.7.What size of force F is required to apply to cause the block to slide downwards at a constant speed? To slide upwards at a constant speed?
To determine the force required to slide the block downwards at a constant speed, we need to analyze the forces acting on the block.
1. Weight of the block: The weight of the block can be calculated by multiplying the mass (5 kg) by the acceleration due to gravity (9.8 m/s^2), giving us a weight of 49 N (Newtons) acting vertically downwards.
2. Force of gravity acting downwards: This force is equal to the weight of the block (49 N).
3. Normal force: The normal force is the force exerted by the wooden wall on the block perpendicular to the surface. As the block is sliding downwards, the normal force is equal in magnitude and opposite in direction to the force of gravity or weight (49 N).
4. Force of friction: The force of friction opposes the motion of the block and is given by the coefficient of kinetic friction (μ) multiplied by the normal force. In this case, the coefficient of kinetic friction is 0.7, so the force of friction is (0.7 * 49 N) = 34.3 N.
Now, let's break the force F into its horizontal and vertical components:
1. Horizontal component: F * cos(40°)
- This component acts parallel to the wooden wall.
2. Vertical component: F * sin(40°)
- This component acts perpendicular to the wooden wall.
To slide the block downwards at a constant speed, the force pushing downwards should overcome the force of gravity and the force of friction. Since the block is not accelerating vertically, the vertical component of force (F * sin(40°)) must be equal to the sum of the weight and the force of friction:
F * sin(40°) = (49 N + 34.3 N)
F * sin(40°) = 83.3 N
Now, we can solve for the force required to slide the block downwards at a constant speed:
F = 83.3 N / sin(40°)
F ≈ 134.3 N
To slide the block upwards at a constant speed (against gravity), the force pushing upwards should be equal to the sum of the weight and the force of friction:
F * sin(40°) = (49 N + 34.3 N)
F * sin(40°) = 83.3 N
Now, we can solve for the force required to slide the block upwards at a constant speed:
F = 83.3 N / sin(40°)
F ≈ 134.3 N
Therefore, the force required to slide the block downwards or upwards at a constant speed is approximately 134.3 N.
To find the size of the force required to cause the block to slide downwards at a constant speed, we need to consider the forces acting on the block.
1. Gravity: The weight of the steel block can be calculated by multiplying its mass (5 kg) by the acceleration due to gravity (9.8 m/s^2). Therefore, the weight (W) is 5 kg * 9.8 m/s^2 = 49 N (downward).
2. Normal force: The normal force (N) is the force exerted by the wooden wall on the block perpendicular to the wall surface. Since the block is sliding downwards, the normal force will be equal to the weight of the block, which is 49 N.
3. Friction force: The friction force (F_friction) opposes the motion of the block and acts parallel to the wall surface. The formula for calculating the friction force is F_friction = μ * N, where μ is the coefficient of kinetic friction and N is the normal force.
Since the block is sliding downwards at a constant speed, the force applied (F) will be equal in magnitude and opposite in direction to the friction force. Therefore, F = F_friction = μ * N.
Substituting the given values:
F = 0.7 * 49 N
F = 34.3 N
Therefore, a force of 34.3 N, directed upwards at an angle of 40° to the horizontal, is required to cause the block to slide downwards at a constant speed.
To slide the block upwards at a constant speed, the force required will be the same as the friction force but in the opposite direction. Therefore, the force required to slide the block upwards at a constant speed is also 34.3 N, directed downwards at an angle of 40° to the horizontal.