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Question
A block of mass 3kg s sliding along the frictionless horizontal surface with a speed of 2m/s.
1. What is the kinetic energy of the block?
2. A wedge is placed in front of the block, forcing the block to climb up the frictionless 30degrees incline and slow to a stop. How far along the incline does the block move before coming to a stop?
1. KE = 0.5M*V^2 = 0.5*3*2^2 = 6 Joules.
2. PE = KE, M*g*h = 6, 3*9.8*h = 6, h = 0.204 m.
sin30 = 0.204/d, d*sin30 = 0.204, d = 0.408 m. = Distance along the incline.
To answer both questions, we need to apply the principles of physics, specifically the concepts of kinetic energy and work.
1. Kinetic Energy:
The kinetic energy (KE) of an object is given by the formula: KE = 0.5 * mass * velocity^2. Here, the mass of the block is 3 kg and the velocity is 2 m/s. Plugging in these values, we can calculate the kinetic energy of the block:
KE = 0.5 * 3 kg * (2 m/s)^2 = 6 J (The unit of kinetic energy is Joules).
2. Distance Traveled:
To determine how far the block moves up the incline before coming to a stop, we need to consider the work-energy principle. According to this principle, the work done on an object equals the change in its kinetic energy. In this case, the work done by the force of gravity is equal to the negative change in kinetic energy since the block slows down and eventually comes to a stop.
The work done against gravity can be calculated using the formula: Work = force * distance * cos(angle), where:
- force is the component of the gravitational force acting parallel to the incline, which is given by: force = mass * gravitational acceleration * sin(angle).
- distance is the distance moved up the incline.
- angle is the angle of the incline, given as 30 degrees.
Since the gravitational force is opposing the motion, the work done by gravity is negative. Therefore, we can equate the work done by gravity to the negative change in kinetic energy.
Change in kinetic energy = -Work
Change in kinetic energy = -force * distance * cos(angle)
To find the distance moved up the incline, we rearrange the equation:
distance = -(Change in kinetic energy) / (force * cos(angle))
We know the change in kinetic energy from the previous question is 6 J, and we can substitute the values of mass (3 kg) and gravitational acceleration (9.8 m/s^2). Plugging in these values, we have:
distance = -6 J / (3 kg * 9.8 m/s^2 * cos(30 degrees))
Evaluating this equation will give us the distance traveled by the block up the incline before coming to a stop.