Cn u plz gv explaination 2 d solutions steps by steps briefly?Cz i really dnt understand hw 2 apply d formula wen i revise it nw. Much appreciated. [g=10 m/s^2 ] a fixed wedge whose smooth sloping face is inclined at 30 degree to the horizontal. A particle A, of mass 2 kg, rests on the sloping face of the wedge. A light inextensible string, passes over a smooth pulley at the top of the wedge & connects A to a particle B,of mass 3kg, which hangs freely. The sloping part of the string is parallel to a line of greatest slope,is applied to A. Assuming that A has not reached the bottom of the slope & B has not reached the pulley, calculate (a) the tension in the string, (b) the work done by the 25 N force while the speed of the particles increases from 1 m/s to 3 m/s.Ans: (a)33 N (b)100J
To calculate the tension in the string and the work done by the force, we can follow these steps:
Step 1: Determine the forces acting on each object.
- Particle A on the wedge experiences its weight (mg) and the tension in the string (T).
- Particle B experiences its weight (mg).
Step 2: Draw a free-body diagram for both objects.
- For Particle A, the weight (mg) acts vertically downwards, and the tension (T) acts parallel to the slope.
- For Particle B, the weight (mg) acts vertically downwards.
Step 3: Break down the forces along the x and y axis for Particle A.
- The weight (mg) can be divided into two components: mg*sin(30°) along the slope and mg*cos(30°) perpendicular to the slope.
- The tension (T) is parallel to the slope.
Step 4: Write down the equations for the forces.
- Along the x-axis: T = ma (where "a" is the acceleration of A along the slope).
- Along the y-axis: N - mg*cos(30°) = 0 (where N is the normal force exerted by the wedge).
Step 5: Solve for the unknowns.
- From the equation along the y-axis, N = mg*cos(30°).
- Substitute this value into the equation along the x-axis: T = ma.
- Now, substitute for "a" using a = g*sin(30°).
- T = m * g * sin(30°).
Step 6: Plug in the given values.
- Given: m = 2 kg, g = 10 m/s^2.
- T = 2 * 10 * sin(30°)
- T = 20 * 0.5
- T = 10 N.
Thus, the tension in the string is 10 N, as calculated.
Now, to calculate the work done by the 25 N force:
Step 7: Calculate the change in kinetic energy.
- The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
- The change in kinetic energy can be calculated using the equation: ΔKE = (1/2) * m * (v^2 - u^2).
Step 8: Plug in the given values.
- Given: m = 3 kg, u = 1 m/s, v = 3 m/s.
- ΔKE = (1/2) * 3 * (3^2 - 1^2)
- ΔKE = (1/2) * 3 * (9-1)
- ΔKE = (1/2) * 3 * 8
- ΔKE = 12 J.
Thus, the work done by the 25 N force is 12 J, as calculated.
In summary:
(a) The tension in the string is 10 N.
(b) The work done by the 25 N force is 12 J.