A child swinging on a tyre swing mas a mass of 30 kg and is moving at a speed of v = 4 m/s when the swing reaches its lowest point at θ = 0∘. Assuming that the size of the child and tyre swing is small with respect to the length of the swing (and can hence be approximated as a particle) and the length of the cord l = 4 m, determine: i. The tension in the cord at θ = 0∘ (5 marks) ii. The maximum angle θ that the child swings to and momentarily stops (10 marks) iii. The tension in the rope holding the swing at this instant (10 marks)
A child of mass 26 kg swings at the end of an elastic cord. At the bottom of the swing, the child's velocity is horizontal, and the speed is 7 m/s. At this instant the cord is 4.50 m long. (Take the +x direction to be horizontal and to the right, the +y direction to be upward, and the +z direction to be out of the page.) (a) At this instant, what is the parallel component of the rate of change of the child's momentum? d|p→| dtp^ = (kg⋅m/s)/s (b) At this instant, what is the perpendicular component of the rate of change of the child's momentum? |p→|dρ^ dt = (kg⋅m/s)/s (c) At this instant, what is the net force acting on the child? F→net = N (d) What is the magnitude of the force that the elastic cord exerts on the child? (It helps to draw a diagram of the forces.) |F→due to cord | = N (e) The relaxed length of the elastic cord is 4.43 m. What is the stiffness of the cord? (Use the exact value you entered in part (d) to make this calculation.) ks = N/m
Figure 5 shows two masses, MA = 3 kg and MB = 2 kg are tied to a same string that run through a pulley. An external force, F is applied, pulling down the mass B. Given that, the common acceleration of the two masses is 4.5 m/s2 and the coefficient of friction is μk = 0.05. (a) Draw free body diagram for both masses. (b) Find the normal force and the tension of the string. (c) Find the external force, F applied to mass B.
A gymnast is swinging on a high bar. The distance between his waist and the bar is 0.990 m, as the drawing shows. At the top of the swing his speed is momentarily zero. Ignoring friction and treating the gymnast as if all of his mass is located at his waist, find his speed at the bottom of the swing. Number Units
When the three blocks in the figure are released from rest, they accelerate with a magnitude of 0.600 m/s2. Block 1 has mass M, block 2 has 2M, and block 3 has 2M. What is the coefficient of kinetic friction between block 2 and the table? Number Units
A 850-kg race car can drive around an unbanked turn at a maximum speed of 43 m/s without slipping. The turn has a radius of 190 m. Air flowing over the car's wing exerts a downward-pointing force (called the downforce) of 11000 N on the car. (a) What is the coefficient of static friction between the track and the car's tires? (b) What would be the maximum speed if no downforce acted on the car? (a) Number Units (b) Number Units
A block of mass m = 2.60 kg is pushed a distance d = 2.60 m along a frictionless horizontal table by a constant applied force of magnitude F = 16.0 N directed at an angle θ = 27.0∘ below the horizontal as shown in the figure below. (a) Determine the work done on the block by the applied force. (b) Determine the work done on the block by the normal force exerted by the table. (c) Determine the work done on the block by the force of gravity. (d) Determine the work done by the net force on the block. J
A force is applied horizontally to a block to move it up a 30∘ incline. The incline is frictionless. If F = 50.0 N and M = 6.5 kg, what is the magnitude of the acceleration of the block? |a→| = m/s2
The drawing shows a thin, uniform rod, which has a length of 0.56 m and a mass of 0.0693 kg. This rod is attached to the floor by a hinge at point P. A uniform magnetic field of 0.24 T is directed perpendicular to the rod, as shown. There is a current I = 2.9 A in the rod, which does not rotate clockwise or counterclockwise. Find the angle θ. (Hint: The magnetic force may be taken to act at the center of gravity.) Number Units
The current in a 55-Ω resistor is 0.16 A. This resistor is in series with a 34-Ω resistor, and the series combination is connected across a battery. What is the battery voltage? Number Units
A charged particle enters a uniform magnetic field and follows the circular path shown in the drawing. The particle's speed is 163 m/s, the magnitude of the magnetic field is 0.228 T, and the radius of the path is 733 m. Determine the mass of the particle, given that its charge has a magnitude of 7.69×10−4 C Number Units
A 53.8-kg box is being pushed a distance of 6.60 m across the floor by a force P→ whose magnitude is 166 N. The force P→ is parallel to the displacement of the box. The coefficient of kinetic friction is 0.228. Determine the work done on the box by each of the four forces that act on the box. Be sure to include the proper plus or minus sign for the work done by each force. (a) WP = (b) Wf = (c) Wmg = (d) WN =
The skateboarder in the drawing starts down the left side of the ramp with an initial speed of 6.1 m/s. Neglect nonconservative forces, such as friction and air resistance, and find the height h of the highest point reached by the skateboarder on the right side of the ramp.
In a certain region, the earth's magnetic field has a magnitude of 5.4×10−5 T and is directed north at an angle of 45∘ below the horizontal. An electrically charged bullet is fired north and 18∘ above the horizontal, with a speed of 540 m/s. The magnetic force on the bullet is 3.2×10−10 N, directed due east. Determine the bullet's electric charge, including its algebraic sign (+ or -). Number Units
Block and three cords. In the figure below, a block B of mass M = 24.9 kg hangs by a cord from a knot K of mass mK, which hangs from a ceiling by means of two cords. The cords have negligible mass, and the magnitude of the gravitational force on the knot is negligible compared to the gravitational force on the block. The angles are θ1 = 24.0∘ and θ2 = 51.0∘. What is the tension in (a) cord 3, (b) cord 1, and (c) cord 2?
A platform of mass M = 4 kg lies on the floor with coefficient of static friction between floor and platform μs = 0,1. On the platform is a box with mass m = 1 kg. Surface between the box and platform is frictionless, a massless spring attaches the box to the platform that has spring constant of k = 400 N/m. Innitially the box is at rest but then it is pressed to the right so itreceivesan initial velocity of V (a) What is the equation for the maximum force of the spring as a function of V? (b) What is the maximum value of V so the platform stays motionless?
The figure below shows two point charges q1 = +5.1×10-8 C and q2 = -5.5×10-8 C. (a) Find the potential at A. (b) Find the potential at B. (c) Find the potential difference VA - VB.
Multiple-Concept Example 13 presents useful background for this problem. The cheetah is one of the fastest accelerating animals, for it can go from rest to 27.4 m/s in 3.07 s. If its mass is 118 kg, determine the average power developed by the cheetah during the acceleration phase of its motion. Express your answer in (a) watts and (b) horsepower. (a) Number Units (b) Number Units
Consider the three charges q1 = q2 = 7q and q3 = −q. Which of the following configurations will result in an electric flux of 6q/ε0 through the enclosed surface? Select all that apply.
You are performing studies of the possibility of migrating birds using the Earth's magnetic field for navigation. To modify the magnetic field in the brain of a bird, you fit the bird with coils as "caps" and "collars" as shown in the figure below. The data on the coils indicate that they each have 210 Ω of resistance, a radius of 1.25 cm, and 50 turns of wire. The centers of the coils are separated by 2.25 cm. You wish to create an "Earth-like" magnetic field of 6.0×10−5 T at the midpoint of the axis between the coils. Given this data, you need to determine the voltage of the battery (in V) needed to power the coils. V