A 500g trolly is placed on a runway that is tilted so that it makes an angle of 30 degrees to a horizontal table.A light inextensible string is attached to 150g mass piece.the trolly accelerates down the slope as a result of the force applied by the hanging mass piece.the frictional force between the trolly and the runway is 1.5N
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T =418,43
To find the acceleration of the trolley, we need to consider the forces acting on it.
1. Gravity: The force of gravity acting vertically downward can be calculated by multiplying the mass of the trolley (0.5 kg) by the acceleration due to gravity (9.8 m/s²). Therefore, the force of gravity is 0.5 kg * 9.8 m/s² = 4.9 N.
2. Normal force: The normal force is the force exerted by a surface perpendicular to the surface. In this case, the normal force equals the gravitational force acting on the trolley since it is on a horizontal table. Therefore, the normal force is 4.9 N.
3. Frictional force: The frictional force between the trolley and the runway is given as 1.5 N.
4. Force due to the hanging mass piece: The force cause the acceleration of the trolley is the force applied by the hanging mass piece. This force can be calculated by multiplying the mass of the hanging mass piece (0.15 kg) by the acceleration due to gravity (9.8 m/s²). Therefore, the force applied is 0.15 kg * 9.8 m/s² = 1.47 N.
Now let's use these forces to find the acceleration of the trolley. We'll assume the positive direction is downwards.
The net force acting on the trolley can be calculated by subtracting the frictional force from the component of the force due to the hanging mass piece acting in the direction of the slope:
Net force = Force due to hanging mass piece - Frictional force
= 1.47 N - 1.5 N
= -0.03 N (negative sign because the forces are in opposite directions)
Using Newton's second law of motion, we know that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
Net force = (Mass of the trolley + Mass of the hanging mass piece) * Acceleration
Rearranging the equation, we can solve for acceleration:
Acceleration = Net force / (Mass of the trolley + Mass of the hanging mass piece)
= -0.03 N / (0.5 kg + 0.15 kg)
= -0.03 N / 0.65 kg
= -0.0462 m/s²
Therefore, the acceleration of the trolley is approximately -0.0462 m/s² (negative sign indicates that the trolley is accelerating in the opposite direction of the hanging mass piece).