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A baseball rolls off a 0.70 m high desk and strikes the floor 0.25 m away from the base of the desk. How fast was the ball rolling?
A \( 2 \, \text{kg}\) mass is attached to a spring with spring constant \( k = 100 \, \text{N/m}\) and negligible mass.
A \( 15 \) \( \text{N} \) force is pushing a \( 40 \) \( \text{N} \) block down a incline. The angle of the inline is \( \alpha = 40^{\circ} \). The coefficient of static friction between the block and the incline is \( \mu_s = 0.75 \) and the coefficient of kinetic friction is \( \mu_k = 0.65 \).
A block of mass \( 4.0 \) \( \text{kg} \) rests on an inclined plane. The coefficient of static friction between the block and the plane \( \mu_s \) is \( 0.4 \). Which of the following gives the angle of inclination at which the block will start to slide?
Three forces of equal magnitude are applied to a \(3 \, \text{m} \times 2 \, \text{m}\) rectangle. Force \(F_1\) and \(F_2\) act at \(45^\circ\) angles to the vertical as shown, while \(F_3\) acts horizontally.
In short:
\(F_1\): applied at \((0, -2)\), direction SW \(45^\circ\)
\(F_2\): applied at \((2, -2)\), direction NW \(45^\circ\)
\(F_3\): applied at \((3, -1)\), direction east
Points of rotation: \(A = (0, 0)\), \(B = (0, -1)\), \(C = (1, -1)\)
A cat chases a mouse across a \(1.0 \, \text{m}\) high table. The mouse steps out of the way, and the cat slides off the table and strikes the floor \(2.2 \, \text{m}\) from the edge of the table. When the cat slid off the table, what was its speed?
A projectile is launched at angle \( \theta \) to the horizontal, with velocity \( v \), maximum vertical displacement \( s \), and angle \( \theta \) between \( 0^{\circ} \) and \( 45^{\circ} \). What will the maximum vertical displacement be if the projectile is now launched at an angle of \( 2 \theta \) from the horizontal with velocity \( v \)?
Flywheels (rapidly rotating disks) are widely used in industry for storing energy. They are spun up slowly when extra energy is available, then decelerate quickly when needed to supply a boost of energy. A flywheel, \( 20 \text{ cm} \) in diameter, can spin at \( 20{,}000 \text{ rpm} \).
The system above is NOT balanced since \(m_2\) is twice the mass of \(m_1\). Which of the following changes would NOT balance the system so that there is 0 net torque? Assume the plank has no mass of its own.
The figure shows a person’s foot. In that figure, the Achilles tendon exerts a force of magnitude F = 720 N. What is the magnitude of the torque that this force produces about the ankle joint?
A force \(F\) is used to hold a block of mass \(m\) on an incline as shown in the diagram above. The plane makes an angle of \(\theta\) with the horizontal and \(F\) is perpendicular to the plane. The coefficient of friction between the plane and the block is \(\mu\). What is the minimum force \(F\) necessary to keep the block at rest?
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