A hot-air balloonist, rising vertically with a constant velocity of magnitude 5.00 m/s, releases a sandbag at an instant when the balloon is 40.0 m above the ground. After the sandbag is released, it is in free fall. (a) Compute the position and velocity of the sandbag at 0.250 s and 1.00 s after its release. (b) How many seconds after its release does the bag strike the ground? (c) With what magnitude of velocity does it strike the ground? (d) What is the greatest height above the ground that the sandbag reaches? (e) Sketch , and y-t graphs for the motion.
The rope and pulley have negligible mass, and the pulley is frictionless. The coefficient of kinetic friction between the
8.00-kg block and the tabletop is . The blocks are released from rest. Use energy methods to calculate the speed of the 6.00-kg block after it has descended 1.50 m.
A bicycle with 0.80-m-diameter tires is coasting on a level road at 5.6 m/s. A small blue dot has been painted on the tread of the rear tire. a. What is the angular speed of the tires? b. What is the speed of the blue dot when it is 0.80 m above the road? c. What is the speed of the blue dot when it is 0.40 m above the road?
A hollow, conducting sphere with an outer radius of 0.250 m and an inner radius of 0.200 m has a uniform surface charge destiny of . A charge of is now introduced at the center of the cavity inside the sphere.
(a) What is the new carge density on the outside of the sphere?
(b) Calculate the strength of the electric field just outside the sphere.
(c) What is the electric flux through a spherical surface just inside the inner surface of the sphere?
An antelope moving with constant acceleration covers the distance between two points 70.0 m apart in 6.00 s. Its speed as it passes the second point is 15.0 m/s. What are (a) its speed at the first point and (b) its acceleration?
A fan blade rotates with angular velocity given by , where and . (a) Calculate the angular acceleration as a function of time. (b) Calculate the instantaneous angular acceleration at at t = 3.00 s and the average angular acceleration for the time interval t = 0 to t = 3.00 s. How do these two quantities compare? If they are different, why?
The mass of Venus is 81.5% that of the earth, and its radius is 94.9% that of the earth.
(a) Compute the acceleration due to gravity on the surface of Venus from these data.
(b) If a rock weighs 75.0 N on earth, what would it weigh at the surface of Venuse?
The air pressure in the tires of a car is . Determine the average area of contact of each tire with the road.
It takes the elevator in a skyscraper 4.0 s to reach its cruising speed of 10 m/s. A 60 kg passenger gets aboard on the ground floor. What is the passengers
A jet plane lands with a speed of 100 m/s and can accelerate at a maximum rate of as it comes to rest. Can this plane land on a small tropical island airport where the runway is 0.800 km long?
In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints to a speed of 6.0 m/s in 1.5 s. Assuming that the player accelerates uniformly, determine the distance he runs.
An oil pump is drawing 44 kW of electric power while pumping oil with ρ= 860 kg/m^3 at a rate of 0.1 m^3/s. The inlet and outlet diameters of the piper are 8 cm and 12 cm, respectively. If the pressure rise of oil in the pump is measured to be 500 kPa and the motor efficiency is 90 percent, determine the mechanical efficiency of the pump.
A water pump that consumes 2 kW of electric power when operating is claimed to take in water from a lake and pump it to a pool whose free surface is 30 m above the free surface of the lake at a rate of 50 L/s. Determine if this claim is reasonable.
A rocket starts from rest and moves upward from the surface of the earth. For the first 10.0 s of its motion, the vertical acceleration of the rocket is given by )t, where the + y-direction is upward. (a) What is the height of the rocket above the surface of the earth at t = 10.0 s? (b) What is the speed of the rocket when it is 325 m above the surface of the earth?
A horizontal rope is tied to a 50 kg box on frictionless ice. What is the tension in the rope if a. The box is at rest? b. The box moves at a steady 5.0 m/s? c. The box has and
A bicycle wheel has an initial angular velocity of 1.50 rad/s. (a) If its angular acceleration is constant and equal to , what is its angular velocit at t=2.50 s? (b) Through what angle has the wheel turned between t = 0 and t = 2.50 s?
At a certain location, wind is blowing steadily at 10 m/s. Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 60-m-diameter blades at that location. Take the air density to be .
Boxes A and B are in contact on a horizontal, frictionless surface. Box A has mass 20.0 kg and box B has mass 5.0 kg. A horizontal force of 250 N is exerted on box A. What is the magnitude of the force that box A exerts on box B?
The best leaper in the animal kingdom is the puma, which can jump to a height of 3.7 m when leaving the ground at an angle of . With what speed must the animal leave the ground to reach that height?
The wave function for a traveling wave on a taut string is (in SI units)(a) What are the speed and direction of travel of the wave? (b) What is the vertical position of an element of the string at t = 0, x = 0.100 m? What are (c) the wavelength and (d) the frequency of the wave? (e) What is the maximum transverse speed of an element of the string?