a block of mass 5 kg is position at angle 45 degree ,a force of 10 newton is applied to the block parallel to the ground. is the coefficient of kinetic friction is 0.5 , calculate its acceleration?
To calculate the acceleration, we need to consider the forces acting on the block. The applied force parallel to the ground will contribute to the acceleration, while the force of friction will oppose the motion and reduce the acceleration.
First, let's resolve the applied force into horizontal and vertical components. Since the force is parallel to the ground and the block is at an angle of 45 degrees, both components will have the same magnitude.
The vertical component of the force can be found using trigonometry:
Vertical component = force * sin(angle)
= 10 N * sin(45°)
= 10 N * 0.707
= 7.07 N
The horizontal component of the force can also be calculated using trigonometry:
Horizontal component = force * cos(angle)
= 10 N * cos(45°)
= 10 N * 0.707
= 7.07 N
Now, let's calculate the force of friction opposing the motion. The force of friction can be found using the equation:
Force of friction = coefficient of friction * Normal force
The normal force is the force exerted by the surface on the block, perpendicular to the surface. In this case, the normal force would be equal to the weight of the block, which can be calculated using the equation:
Weight = mass * gravitational acceleration
Weight = 5 kg * 9.8 m/s²
= 49 N
Therefore, the normal force is 49 N. Now we can calculate the force of friction:
Force of friction = 0.5 * 49 N
= 24.5 N
Since the force of friction opposes the motion, we need to subtract it from the horizontal component of the applied force to find the net force:
Net force = horizontal component of applied force - force of friction
= 7.07 N - 24.5 N
= -17.43 N
Finally, using Newton's second law of motion (F = ma), we can calculate the acceleration:
Acceleration = Net force / mass
= -17.43 N / 5 kg
= -3.486 m/s²
Therefore, the acceleration of the block is approximately -3.486 m/s². The negative sign indicates that the acceleration is in the opposite direction of the applied force.