Physics Problems

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  1. A box is being pulled with force F\(_a\) = 40 N at an angle \(\theta\) = 30 degrees. There is a frictional force opposing the sliding of the box with force F\(_f\) = 10 N. Draw a free body diagram to help answer the following questions. (use gravity at 10m/s\(^2\) to simplify the numbers)

    Free body diagram physics example problem

    • Define the X and Y directions.
    • Resolve all forces into X and Y components.
    • Find the acceleration of the box.

  2. A 5 kg lawn mower is being pushed with an applied force of F\(_a\) = 20 N, at an angle of \(\theta\) . There is a frictional force, F\(_f\) opposing the movement of the lawn mower of 10 N. Given that the lawn mower is accelerating at 0.4 m/s\(^2\):

    Free body diagram physics example problem

    • Find the angle \(\theta\)
    • Find the magnitude of the normal force, F\(_N\)

  3. A block of mass \(m\) is pulled along a rough horizontal surface by a constant applied force of magnitude \(F_1\) that acts at an angle \(\theta\) to the horizontal, as indicated below. The acceleration of the block is \(a_1\) . Express all algebraic answers in terms of \(m\) , \(F_1\) , \(\theta\) , \(a_1\) , and fundamental constants.

    Physics Dynamics Practice

    • Draw and label a free-body diagram showing all the forces on the block.
    • Derive an expression for the normal force exerted by the surface on the block.
    • Derive an expression for the coefficient of kinetic friction \(\mu\) between the block and the surface.
    • Sketch graphs of the speed \(v\) and displacement \(x\) of the block as function of time \(t\) if the block started from rest at \(x\) = 0 and \(t\) = 0.
    • If the applied force is large enough, the block will lose contact with the surface. Derive an expression for the magnitude of the greatest acceleration \(a_{max}\) that the block can have and still maintain contact with the ground.

  4. A rubber ball of mass \(m\) is dropped from a cliff. As the ball falls, it is subject to air drag (a resistive force caused by the air). The drag force on the ball has a magnitude \(bv^2\) , where \(b\) is a constant drag coefficient and \(v\) is the instantaneous speed of the ball. The drag coefficient \(b\) is directly proportional to the cross-sectional area of the ball and the density of the air and does not depend on the mass of the ball. As the ball falls, its speed approaches a constant value called the terminal speed.

    • Draw and label all the forces on the ball at some instant before it reaches terminal speed.
    • State whether the magnitude of the acceleration of the ball of mass \(m\) increases, decreases, or remains the same as the ball approaches terminal speed. Explain.
    • Write, but do NOT solve, a differential equation for the instantaneous speed \(v\) of the ball in terms of time \(t\) , the given quantities, and fundamental constants.
    • Determine the terminal speed \(v_t\) in terms of the given quantities and fundamental constants.
    • Determine the energy dissipated by the drag force during the fall if the ball is released at height \(h\) and reaches its terminal speed before hitting the ground, in terms of the given quantities and fundamental constants. (this question requires knowledge of potential and kinetic energy, often not introduced until later in a physics course)

  5. What is the tension T in the rope if the 10-N weight is moving upward with a constant velocity?

    MCAT practice

  6. A car of mass 100 kg is traveling in a circle of radius 20 m. There is a frictional force of 500 N on the car's wheels (in the direction of the center of the circle, to keep the car going in a circle). Draw a free body diagram for the car and find the velocity of the car.

  7. A student is swinging a mass, m = 2.0 kg, in a uniform vertical circle of radius R = 2.5 m. The period of the rotation is 2.8 seconds. Draw a free body diagram for the mass at the top of the circle and find the tension of the string (ignore friction and the mass of the string.) Repeat for the mass at the bottom of the rotation.

  8. A car is driving in a circle on an embanked road as shown below. Draw a free body diagram for the car, ignoring friction.

    centripetal acceleration physics problem

  9. A 1.2 kg mass, m, is swinging on a string pendulum of length 80 cm (the string has negligible mass). As shown in the figure below, when \(\theta\) is 10 degrees the velocity of the mass is 0.6 m/s. Find the tension in the string and the acceleration of the mass at this moment.

    centripetal acceleration pendulum physics problem

  10. Given that the radius of orbit for the moon is 3.8 x 10\(^8\) m, the period of the moon's orbit is 2.36 x 10\(^6\) s, and the radius of the earth is 6.38 x 10\(^6\) m; Find the altitude of a geostationary satellite.(hint: use Kepler's third law.)

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